SOLUTION: At a well known university, ¼ of the undergraduate students commute and 1/3 of the graduate students commute. One-tenths of the undergraduate students drive more than 40 miles dail

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Question 148751: At a well known university, ¼ of the undergraduate students commute and 1/3 of the graduate students commute. One-tenths of the undergraduate students drive more than 40 miles daily and 1/6 of the graduate students drive more than 40 miles daily. If there are twice as many undergraduate students as there are graduate students, then what fraction of the commuters drive more than 40 miles daily? Please help? Is this how to do it?
The fraction of the undergraduate and graduate students who commute is represented by 1/4x +1/3x divided by 1/10x +40 divided by 1/6x + 40. (I'm stuck)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
At a well known university, ¼ of the undergraduate students commute and 1/3 of the graduate students commute. One-tenths of the undergraduate students drive more than 40 miles daily and 1/6 of the graduate students drive more than 40 miles daily. If there are twice as many undergraduate students as there are graduate students, then what fraction of the commuters drive more than 40 miles

Here's what I would do:
Choose a convenient number for the total students: 720 has a lot of factors
:
It says,"there are twice as many undergrads as there are grad students,"
That would give us us 480 undergrads, and 240 grads (for a total of 720)
:
1/4 of the undergraduates commute;
1%2F4 * 480 = 120
:
1/3 of the graduates commute.
1%2F3 * 240 = 80
:
1/10 of the undergraduates drive more than 40 miles daily
1%2F10 * 480 = 48
:
1/6 of the graduates drive more than 40 miles daily.
1%2F6 * 240 = 40
:
what fraction of the commuters drive more than 40 miles daily?
:
Total commuters: 120 + 80 = 200
:
Total commuters drive more than 40 mi: 48 + 40 = 88
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Then: 88%2F200 = 11%2F25 of the commuters commute over 40 mi
:
I tried to reply to your email but it kicked it back. Hopefully you will get my
reply here.
:
"Actually I choose it because it was a multiple of all the denominators
involved. 4*3*10*6; insuring that all the values would be integers. (I
should have explained that). Another value could have been used, since they
are not asking for the actual number of students, but just the relationships
(fraction) to the various student groups. Did this make sense to you?"""
:
Let me know if you received this please.